Transversely-excited film bulk acoustic resonator with multiple diaphragm thicknesses and fabrication method

ABSTRACT

Filter devices and methods are disclosed. A filter device includes a substrate having a surface. A back surface of a single-crystal piezoelectric plate is attached to the surface of the substrate, portions of the single-crystal piezoelectric plate forming a plurality of diaphragms spanning respective cavities in the substrate. A conductor pattern is formed on a front surface of the piezoelectric plate, the conductor pattern including a plurality of interdigital transducers (IDTs) of a plurality of resonators. Interleaved fingers of at least a first IDT of the plurality of IDTs are disposed on a diaphragm having a first thickness, and interleaved fingers of at least a second IDT of the plurality of IDTs are disposed on a diaphragm having a second thickness less than the first thickness.

RELATED APPLICATION INFORMATION

The patent claims priority to the following provisional patent applications: application 62/892,980, titled XBAR FABRICATION, filed Aug. 28, 2019; and application 62/904,152, titled DIELECTRIC OVELAYER TRIMMING FOR FREQUENCY CONTROL, filed Sep. 23, 2019.

This patent is a continuation in part of application Ser. No. 16/438,121, filed Jun. 11, 2019, entitled TRANSVERSELY-EXCITED FILM BULK ACOUSTIC RESONATOR, now U.S. Pat. No. 10,756,697, which is a continuation-in-part of application Ser. No. 16/230,443, filed Dec. 21, 2018, entitled TRANSVERSELY-EXCITED FILM BULK ACOUSTIC RESONATOR, now U.S. Pat. No. 10,491,192, which claims priority from the following provisional patent applications: application 62/685,825, filed Jun. 15, 2018, entitled SHEAR-MODE FBAR (XBAR); application 62/701,363, filed Jul. 20, 2018, entitled SHEAR-MODE FBAR (XBAR); application 62/741,702, filed Oct. 5, 2018, entitled 5 GHZ LATERALLY-EXCITED BULK WAVE RESONATOR (XBAR); application 62/748,883, filed Oct. 22, 2018, entitled SHEAR-MODE FILM BULK ACOUSTIC RESONATOR; and application 62/753,815, filed Oct. 31, 2018, entitled LITHIUM TANTALATE SHEAR-MODE FILM BULK ACOUSTIC RESONATOR. All of these applications are incorporated herein by reference.

NOTICE OF COPYRIGHTS AND TRADE DRESS

A portion of the disclosure of this patent document contains material which is subject to copyright protection. This patent document may show and/or describe matter which is or may become trade dress of the owner. The copyright and trade dress owner has no objection to the facsimile reproduction by anyone of the patent disclosure as it appears in the Patent and Trademark Office patent files or records, but otherwise reserves all copyright and trade dress rights whatsoever.

BACKGROUND Field

This disclosure relates to radio frequency filters using acoustic wave resonators, and specifically to filters for use in communications equipment.

Description of the Related Art

A radio frequency (RF) filter is a two-port device configured to pass some frequencies and to stop other frequencies, where “pass” means transmit with relatively low signal loss and “stop” means block or substantially attenuate. The range of frequencies passed by a filter is referred to as the “pass-band” of the filter. The range of frequencies stopped by such a filter is referred to as the “stop-band” of the filter. A typical RF filter has at least one pass-band and at least one stop-band. Specific requirements on a pass-band or stop-band depend on the specific application. For example, a “pass-band” may be defined as a frequency range where the insertion loss of a filter is better than a defined value such as 1 dB, 2 dB, or 3 dB. A “stop-band” may be defined as a frequency range where the rejection of a filter is greater than a defined value such as 20 dB, 30 dB, 40 dB, or greater depending on application.

RF filters are used in communications systems where information is transmitted over wireless links. For example, RF filters may be found in the RF front-ends of cellular base stations, mobile telephone and computing devices, satellite transceivers and ground stations, IoT (Internet of Things) devices, laptop computers and tablets, fixed point radio links, and other communications systems. RF filters are also used in radar and electronic and information warfare systems.

RF filters typically require many design trade-offs to achieve, for each specific application, the best compromise between performance parameters such as insertion loss, rejection, isolation, power handling, linearity, size and cost. Specific design and manufacturing methods and enhancements can benefit simultaneously one or several of these requirements.

Performance enhancements to the RF filters in a wireless system can have broad impact to system performance. Improvements in RF filters can be leveraged to provide system performance improvements such as larger cell size, longer battery life, higher data rates, greater network capacity, lower cost, enhanced security, higher reliability, etc. These improvements can be realized at many levels of the wireless system both separately and in combination, for example at the RF module, RF transceiver, mobile or fixed sub-system, or network levels.

The desire for wider communication channel bandwidths will inevitably lead to the use of higher frequency communications bands. The current LTE™ (Long Term Evolution) specification defines frequency bands from 3.3 GHz to 5.9 GHz. These bands are not presently used. Future proposals for wireless communications include millimeter wave communication bands with frequencies up to 28 GHz.

High performance RF filters for present communication systems commonly incorporate acoustic wave resonators including surface acoustic wave (SAW) resonators, bulk acoustic wave (BAW) resonators, film bulk acoustic wave resonators (FBAR), and other types of acoustic resonators. However, these existing technologies are not well-suited for use at the higher frequencies proposed for future communications networks.

DESCRIPTION OF THE DRAWINGS

FIG. 1 includes a schematic plan view and two schematic cross-sectional views of a transversely-excited film bulk acoustic resonator (XBAR).

FIG. 2 is an expanded schematic cross-sectional view of a portion of the XBAR of FIG. 1.

FIG. 3 is an alternative schematic cross-sectional view of the XBAR of FIG. 1.

FIG. 4 is a graphic illustrating a shear acoustic mode in an XBAR.

FIG. 5 is a schematic block diagram of a bandpass filter incorporating seven XBARs.

FIG. 6A is a schematic cross-sectional view of a filter with a dielectric layer to set a frequency separation between shunt resonators and series resonators.

FIG. 6B is a schematic cross-sectional view of a filter with different piezoelectric diaphragm thicknesses to set a frequency separation between shunt resonators and series resonators.

FIG. 7 is a series of schematic cross-section views illustrating a process to control the thickness of a piezoelectric diaphragm.

FIG. 8 is a flow chart of a process for fabricating a filter implemented with XBARs.

FIG. 9 is a flow chart of another process for fabricating a filter implemented with XBARs.

FIG. 10 is a flow chart of another process for fabricating a filter implemented with XBARs.

FIG. 11 is a flow chart of another process for fabricating a filter implemented with XBARs.

Throughout this description, elements appearing in figures are assigned three-digit or four-digit reference designators, where the two least significant digits are specific to the element and the one or two most significant digit is the figure number where the element is first introduced. An element that is not described in conjunction with a figure may be presumed to have the same characteristics and function as a previously-described element having the same reference designator.

DETAILED DESCRIPTION Description of Apparatus

FIG. 1 shows a simplified schematic top view and orthogonal cross-sectional views of a transversely-excited film bulk acoustic resonator (XBAR) 100. XBAR resonators such as the resonator 100 may be used in a variety of RF filters including band-reject filters, band-pass filters, duplexers, and multiplexers. XBARs are particularly suited for use in filters for communications bands with frequencies above 3 GHz.

The XBAR 100 is made up of a thin film conductor pattern formed on a surface of a piezoelectric plate 110 having parallel front and back surfaces 112, 114, respectively. The piezoelectric plate is a thin single-crystal layer of a piezoelectric material such as lithium niobate, lithium tantalate, lanthanum gallium silicate, gallium nitride, or aluminum nitride. The piezoelectric plate is cut such that the orientation of the X, Y, and Z crystalline axes with respect to the front and back surfaces is known and consistent. In the examples presented in this patent, the piezoelectric plates are Z-cut, which is to say the Z axis is normal to the surfaces. However, XBARs may be fabricated on piezoelectric plates with other crystallographic orientations.

The back surface 114 of the piezoelectric plate 110 is attached to a substrate 120 that provides mechanical support to the piezoelectric plate 110. The substrate 120 may be, for example, silicon, sapphire, quartz, or some other material. The piezoelectric plate 110 may be bonded to the substrate 120 using a wafer bonding process, or grown on the substrate 120, or attached to the substrate in some other manner. The piezoelectric plate may be attached directly to the substrate, or may be attached to the substrate via one or more intermediate material layers.

The conductor pattern of the XBAR 100 includes an interdigital transducer (IDT) 130. The IDT 130 includes a first plurality of parallel fingers, such as finger 136, extending from a first busbar 132 and a second plurality of fingers extending from a second busbar 134. The first and second pluralities of parallel fingers are interleaved. The interleaved fingers overlap for a distance AP, commonly referred to as the “aperture” of the IDT. The center-to-center distance L between the outermost fingers of the IDT 130 is the “length” of the IDT.

The first and second busbars 132, 134 serve as the terminals of the XBAR 100. A radio frequency or microwave signal applied between the two busbars 132, 134 of the IDT 130 excites an acoustic wave within the piezoelectric plate 110. As will be discussed in further detail, the excited acoustic wave is a bulk shear wave that propagates in the direction normal to the surface of the piezoelectric plate 110, which is also normal, or transverse, to the direction of the electric field created by the IDT fingers. Thus, the XBAR is considered a transversely-excited film bulk wave resonator.

A cavity 140 is formed in the substrate 120 such that a portion 115 of the piezoelectric plate 110 containing the IDT 130 is suspended over the cavity 140 without contacting the substrate 120. “Cavity” has its conventional meaning of “an empty space within a solid body.” The cavity 140 may be a hole completely through the substrate 120 (as shown in Section A-A and Section B-B) or a recess in the substrate 120 (as shown subsequently in FIG. 3). The cavity 140 may be formed, for example, by selective etching of the substrate 120 before or after the piezoelectric plate 110 and the substrate 120 are attached. As shown in FIG. 1, the cavity 140 has a rectangular shape with an extent greater than the aperture AP and length L of the IDT 130. A cavity of an XBAR may have a different shape, such as a regular or irregular polygon. The cavity of an XBAR may more or fewer than four sides, which may be straight or curved.

The portion 115 of the piezoelectric plate suspended over the cavity 140 will be referred to herein as the “diaphragm” (for lack of a better term) due to its physical resemblance to the diaphragm of a microphone. The diaphragm may be continuously and seamlessly connected to the rest of the piezoelectric plate 110 around all, or nearly all, of perimeter of the cavity 140.

For ease of presentation in FIG. 1, the geometric pitch and width of the IDT fingers is greatly exaggerated with respect to the length (dimension L) and aperture (dimension AP) of the XBAR. A typical XBAR has more than ten parallel fingers in the IDT 110. An XBAR may have hundreds, possibly thousands, of parallel fingers in the IDT 110. Similarly, the thickness of the fingers in the cross-sectional views is greatly exaggerated.

FIG. 2 shows a detailed schematic cross-sectional view of the XBAR 100 of FIG. 1. The piezoelectric plate 110 is a single-crystal layer of piezoelectrical material having a thickness ts. ts may be, for example, 100 nm to 1500 nm. When used in filters for LTE™ bands from 3.4 GHZ to 6 GHz (e.g. bands 42, 43, 46), the thickness ts may be, for example, 200 nm to 1000 nm.

A front-side dielectric layer 214 may optionally be formed on the front side of the piezoelectric plate 110. The “front side” of the XBAR is, by definition, the surface facing away from the substrate. The front-side dielectric layer 214 has a thickness tfd. The front-side dielectric layer 214 is formed between the IDT fingers 238. Although not shown in FIG. 2, the front side dielectric layer 214 may also be deposited over the IDT fingers 238. A back-side dielectric layer 216 may optionally be formed on the back side of the piezoelectric plate 110. The back-side dielectric layer 216 has a thickness tbd. The front-side and back-side dielectric layers 214, 216 may be a non-piezoelectric dielectric material, such as silicon dioxide or silicon nitride. tfd and tbd may be, for example, 0 to 500 nm. tfd and tbd are typically less than the thickness ts of the piezoelectric plate. tfd and tbd are not necessarily equal, and the front-side and back-side dielectric layers 214, 216 are not necessarily the same material. Either or both of the front-side and back-side dielectric layers 214, 216 may be formed of multiple layers of two or more materials.

The IDT fingers 238 may be aluminum or a substantially aluminum alloy, copper or a substantially copper alloy, beryllium, gold, or some other conductive material. Thin (relative to the total thickness of the conductors) layers of other metals, such as chromium or titanium, may be formed under and/or over the fingers to improve adhesion between the fingers and the piezoelectric plate 110 and/or to passivate or encapsulate the fingers. The busbars (132, 134 in FIG. 1) of the IDT may be made of the same or different materials as the fingers.

Dimension p is the center-to-center spacing or “pitch” of the IDT fingers, which may be referred to as the pitch of the IDT and/or the pitch of the XBAR. Dimension w is the width or “mark” of the IDT fingers. The IDT of an XBAR differs substantially from the IDTs used in surface acoustic wave (SAW) resonators. In a SAW resonator, the pitch of the IDT is one-half of the acoustic wavelength at the resonance frequency. Additionally, the mark-to-pitch ratio of a SAW resonator IDT is typically close to 0.5 (i.e. the mark or finger width is about one-fourth of the acoustic wavelength at resonance). In an XBAR, the pitch p of the IDT is typically 2 to 20 times the width w of the fingers. In addition, the pitch p of the IDT is typically 2 to 20 times the thickness ts of the piezoelectric slab 212. The width of the IDT fingers in an XBAR is not constrained to one-fourth of the acoustic wavelength at resonance. For example, the width of XBAR IDT fingers may be 500 nm or greater, such that the IDT can be fabricated using optical lithography. The thickness tm of the IDT fingers may be from 100 nm to about equal to the width w. The thickness of the busbars (132, 134 in FIG. 1) of the IDT may be the same as, or greater than, the thickness tm of the IDT fingers.

FIG. 3 is an alternative cross-sectional view along the section plane A-A defined in FIG. 1. In FIG. 3, a piezoelectric plate 310 is attached to a substrate 320. An optional dielectric layer 322 may be sandwiched between the piezoelectric plate 310 and the substrate 320. A cavity 340, which does not fully penetrate the substrate 320, is formed in the substrate under the portion of the piezoelectric plate 310 containing the IDT of an XBAR. The cavity 340 may be formed, for example, by etching the substrate 320 before attaching the piezoelectric plate 310. Alternatively, the cavity 340 may be formed by etching the substrate 320 with a selective etchant that reaches the substrate through one or more openings 342 provided in the piezoelectric plate 310.

The XBAR 300 shown in FIG. 3 will be referred to herein as a “front-side etch” configuration since the cavity 340 is etched from the front side of the substrate 320 (before or after attaching the piezoelectric plate 310). The XBAR 100 of FIG. 1 will be referred to herein as a “back-side etch” configuration since the cavity 140 is etched from the back side of the substrate 120 after attaching the piezoelectric plate 110.

FIG. 4 is a graphical illustration of the primary acoustic mode of interest in an XBAR. FIG. 4 shows a small portion of an XBAR 400 including a piezoelectric plate 410 and three interleaved IDT fingers 430. An RF voltage is applied to the interleaved fingers 430. This voltage creates a time-varying electric field between the fingers. The direction of the electric field is lateral, or parallel to the surface of the piezoelectric plate 410, as indicated by the arrows labeled “electric field”. Due to the high dielectric constant of the piezoelectric plate, the electric field is highly concentrated in the plate relative to the air. The lateral electric field introduces shear deformation, and thus strongly excites a shear-mode acoustic mode, in the piezoelectric plate 410. In this context, “shear deformation” is defined as deformation in which parallel planes in a material remain parallel and maintain a constant distance while translating relative to each other. A “shear acoustic mode” is defined as an acoustic vibration mode in a medium that results in shear deformation of the medium. The shear deformations in the XBAR 400 are represented by the curves 460, with the adjacent small arrows providing a schematic indication of the direction and magnitude of atomic motion. The degree of atomic motion, as well as the thickness of the piezoelectric plate 410, have been greatly exaggerated for ease of visualization. While the atomic motions are predominantly lateral (i.e. horizontal as shown in FIG. 4), the direction of acoustic energy flow of the excited primary shear acoustic mode is substantially orthogonal to the surface of the piezoelectric plate, as indicated by the arrow 465.

Considering FIG. 4, there is essentially no electric field immediately under the IDT fingers 430, and thus acoustic modes are only minimally excited in the regions 470 under the fingers. There may be evanescent acoustic motions in these regions. Since acoustic vibrations are not excited under the IDT fingers 430, the acoustic energy coupled to the IDT fingers 430 is low (for example compared to the fingers of an IDT in a SAW resonator), which minimizes viscous losses in the IDT fingers.

An acoustic resonator based on shear acoustic wave resonances can achieve better performance than current state-of-the art film-bulk-acoustic-resonators (FBAR) and solidly-mounted-resonator bulk-acoustic-wave (SMR BAW) devices where the electric field is applied in the thickness direction. In such devices, the acoustic mode is compressive with atomic motions and the direction of acoustic energy flow in the thickness direction. In addition, the piezoelectric coupling for shear wave XBAR resonances can be high (>20%) compared to other acoustic resonators. Thus high piezoelectric coupling enables the design and implementation of microwave and millimeter-wave filters with appreciable bandwidth.

FIG. 5 is a schematic circuit diagram for a high frequency band-pass filter 500 using XBARs. The filter 500 has a conventional ladder filter architecture including four series resonators 510A, 510B, 510C, 510D and three shunt resonators 520A, 520B, 520C. The four series resonators 510A, 510B, 510C, and 510D are connected in series between a first port and a second port. In FIG. 5, the first and second ports are labeled “In” and “Out”, respectively. However, the filter 500 is symmetrical and either port and serve as the input or output of the filter. The three shunt resonators 520A, 520B, 520C are connected from nodes between the series resonators to ground. All the shunt resonators and series resonators are XBARs. Although not shown in FIG. 5, any and all of the resonators may be divided into multiple sub-resonators electrically connected in parallel. Each sub-resonator may have a respective diaphragm.

The filter 500 may include a substrate having a surface, a single-crystal piezoelectric plate having parallel front and back surfaces, and an acoustic Bragg reflector sandwiched between the surface of the substrate and the back surface of the single-crystal piezoelectric plate. The substrate, acoustic Bragg reflector, and piezoelectric plate are represented by the rectangle 510 in FIG. 5. A conductor pattern formed on the front surface of the single-crystal piezoelectric plate includes interdigital transducers (IDTs) for each of the four series resonators 510A, 510B, 510C, 510D and three shunt resonators 520A, 520B, 520C. All of the IDTs are configured to excite shear acoustic waves in the single-crystal piezoelectric plate in response to respective radio frequency signals applied to each IDT.

In a ladder filter, such as the filter 500, the resonance frequencies of shunt resonators are typically lower than the resonance frequencies of series resonators. The resonance frequency of an SM XBAR resonator is determined, in part, by IDT pitch. IDT pitch also impacts other filter parameters including impedance and power handling capability. For broad-band filter applications, it may not be practical to provide the required difference between the resonance frequencies of shunt and series resonators using only differences in IDT pitch.

As described in U.S. Pat. No. 10,601,392, a first dielectric layer (represented by the dashed rectangle 525) having a first thickness t1 may be deposited over the IDTs of some or all of the shunt resonators 520A, 520B, 520C. A second dielectric layer (represented by the dashed rectangle 515) having a second thickness t2, less than t1, may be deposited over the IDTs of the series resonators 510A, 510B, 510C, 510D. The second dielectric layer may be deposited over both the shunt and series resonators. The difference between the thickness t1 and the thickness t2 defines a frequency offset between the series and shunt resonators. Individual series or shunt resonators may be tuned to different frequencies by varying the pitch of the respective IDTs. In some filters, more than two dielectric layers of different thicknesses may be used as described in co-pending application 16/924,108.

Alternatively or additionally, the shunt resonators 510A, 510B, 510C, 510D may be formed on a piezoelectric plate having a thickness t3 and the series resonators may be fabricated on a piezoelectric plate having a thickness t4 less than t3. The difference between the thicknesses t3 and t4 defines a frequency offset between the series and shunt resonators. Individual series or shunt resonators may be tuned to different frequencies by varying the pitch of the respective IDTs. In some filters, three or more different piezoelectric plate thicknesses may be used to provide additional frequency tuning capability.

FIG. 6A is a schematic cross-sectional view though a shunt resonator and a series resonator of a filter 600A that uses dielectric thickness to separate the frequencies of shunt and series resonators. A piezoelectric plate 610A is attached to a substrate 620. Portions of the piezoelectric plate form diaphragms spanning cavities 640 in the substrate 620. Interleaved IDT fingers, such as finger 630, are formed on the diaphragms. A first dielectric layer 650, having a thickness t1, is formed over the IDT of the shunt resonator. A second dielectric layer 655, having a thickness t2, is deposited over both the shunt and series resonator. Alternatively, a single dielectric layer having thickness t1+t2 may be deposited over both the shunt and series resonators. The dielectric layer over the series resonator may then be thinned to thickness t2 using a masked dry etching process. In either case, the difference between the overall thickness of the dielectric layers (t1+t2) over the shunt resonator and the thickness t2 of the second dielectric layer defines a frequency offset between the series and shunt resonators.

The second dielectric layer 655 may also serve to seal and passivate the surface of the filter 600A. The second dielectric layer may be the same material as the first dielectric layer or a different material. The second dielectric layer may be a laminate of two or more sub-layers of different materials. Alternatively, an additional dielectric passivation layer (not shown in FIG. 6A) may be formed over the surface of the filter 600A. Further, as will be described subsequently, the thickness of the final dielectric layer (i.e. either the second dielectric layer 655 or an additional dielectric layer) may be locally adjusted to fine-tune the frequency of the filter 600A. Thus the final dielectric layer can be referred to as the “passivation and tuning layer”.

FIG. 6B is a schematic cross-sectional view though a shunt resonator and a series resonator of a filter 600B that uses piezoelectric plate thickness to separate the frequencies of shunt and series resonators. A piezoelectric plate 610B is attached to a substrate 620. Portions of the piezoelectric plate form diaphragms spanning cavities 640 in the substrate 620. Interleaved IDT fingers, such as finger 630, are formed on the diaphragms. The diaphragm of the shunt resonator has a thickness t3. The piezoelectric plate 610B is selectively thinned such that the diaphragm of the series resonator has a thickness t4, which is less than t3. The difference between t3 and t4 defines a frequency offset between the series and shunt resonators. A passivation and tuning layer 655 is deposited over both the shunt and series resonators.

A back surface 614 of the piezoelectric plate 610B is also the back surface of the diaphragms spanning the cavities 640. A front surface 665 of a portion 660 of the piezoelectric plate 610B is recessed with respect to a front surface 612 of the piezoelectric plate 610B, which is also the front surface of the diaphragm of the shunt resonator. The recessed portion 660 of the piezoelectric plate has a thickness t4 which is less than the thickness t3 of the piezoelectric plate 610B. The recessed portion 660 of the piezoelectric plate includes the diaphragm of the series resonator.

Description of Methods

FIG. 7 is a series of schematic cross-section views illustrating a process to control the thickness of a piezoelectric diaphragm. View A shows a piezoelectric plate 710 with non-uniform thickness bonded to a substrate 720. The piezoelectric plate 710 may be, for example, lithium niobate or lithium tantalate. The substrate 720 may be a silicon wafer or some other material as previously described. The illustrated thickness variation in the piezoelectric plate 710 is greatly exaggerated. The thickness variation should not exceed 10% of the piezoelectric plate thickness and may be a few percent or smaller.

View B illustrates an optical measurement of the piezoelectric plate thickness using an optical thickness measurement tool 730 including a light source 732 and a detector 734. The optical thickness measurement tool 730 may be, for example, an ellipsometer/reflectometer. The optical thickness measurement tool 730 measures light reflected from the surface of the piezoelectric plate 710 and from the interface between the piezoelectric plate 710 and the substrate 720. The reflections from a particular measurement point on the piezoelectric plate may be measured using multiple light wavelengths, incidence angles, and/or polarization states. The results of multiple measurements are processed to determine the thickness of the piezoelectric plate at the measurement point.

The measurement process is repeated to determine the thickness of the piezoelectric plate at multiple measurement points on the surface of the piezoelectric plate. The multiple points may, for example, form a grid or matrix of measurement points on the surface of the plate. The measurement data can be processed and interpolated to provide a map of the thickness of the piezoelectric plate.

View C illustrates the removal of excess material from the piezoelectric plate using a material removal tool. In this context, “excess material” is defined as portions of the piezoelectric plate that extend beyond a target plate thickness. The excess material to be removed is shaded in view C. The material removal tool may be, for example, a scanning ion mill 740, a tool employing Fluorine-based reactive ion etching, or some other tool. The scanning ion mill 740 scans a beam 745 of high energy ions over the surface of the piezoelectric. The incidence of the ion beam 745 on the piezoelectric plate removes material at the surface by sublimation or sputtering. The ion beam 745 may be scanned over the surface of the piezoelectric plate one or more times in a raster pattern. The ion current or the dwell time of the ion beam 745 may be varied during the raster scan to control the depth of material removed from each point on the piezoelectric plate in accordance with the map of the thickness of the piezoelectric plate. The result is a piezoelectric plate with substantially improved thickness uniformity as shown in view D. The thickness at any point on the piezoelectric plate may be substantially equal to the target plate thickness, where “substantially equal” means equal to the extent possible as limited by the accuracy of the measurement and the capabilities of the material removal tools.

View E illustrates selective removal to thin selected portions of the piezoelectric plate. Selected portions of the piezoelectric plate may be thinned, for example, to provide diaphragms for series resonators as previously shown in FIG. 5B. Selected portions of the piezoelectric plate may be thinned using the scanning ion mill or other scanning material removal tool if the tool has sufficient spatial resolution to distinguish the areas of the piezoelectric plate to be thinned. Alternatively, a scanning or non-scanning material removal tool 750 or an etching process may be used to remove material from portions of the surface of the piezoelectric plate defined by a mask 752. The result is a piezoelectric plate with reduced thickness regions 760 suitable for the diaphragms of series resonators, as shown in view F.

FIG. 8 is a simplified flow chart showing a process 800 for fabricating a filter device incorporating XBARs. Specifically, the process 800 is for fabricating a filter device using a frequency setting dielectric layer over shunt resonators as shown in FIG. 7A. The process 800 starts at 805 with a device substrate and a thin plate of piezoelectric material disposed on a sacrificial substrate. The process 800 ends at 895 with a completed filter device. The flow chart of FIG. 8 includes only major process steps. Various conventional process steps (e.g. surface preparation, cleaning, inspection, baking, annealing, monitoring, testing, etc.) may be performed before, between, after, and during the steps shown in FIG. 8.

While FIG. 8 generally describes a process for fabricating a single filter device, multiple filter devices may be fabricated simultaneously on a common wafer (consisting of a piezoelectric plate bonded to a substrate). In this case, each step of the process 800 may be performed concurrently on all of the filter devices on the wafer.

The flow chart of FIG. 8 captures three variations of the process 800 for making an XBAR which differ in when and how cavities are formed in the device substrate. The cavities may be formed at steps 810A, 810B, or 810C. Only one of these steps is performed in each of the three variations of the process 800.

The piezoelectric plate may be, for example, lithium niobate or lithium tantalate, either of which may be Z-cut, rotated Z-cut, or rotated YX-cut. The piezoelectric plate may be some other material and/or some other cut. The device substrate may preferably be silicon. The device substrate may be some other material that allows formation of deep cavities by etching or other processing.

In one variation of the process 800, one or more cavities are formed in the device substrate at 810A, before the piezoelectric plate is bonded to the substrate at 815. A separate cavity may be formed for each resonator in a filter device. The one or more cavities may be formed using conventional photolithographic and etching techniques. Typically, the cavities formed at 810A will not penetrate through the device substrate, and the resulting resonator devices will have a cross-section as shown in FIG. 3.

At 815, the piezoelectric plate is bonded to the device substrate. The piezoelectric plate and the device substrate may be bonded by a wafer bonding process. Typically, the mating surfaces of the device substrate and the piezoelectric plate are highly polished. One or more layers of intermediate materials, such as an oxide or metal, may be formed or deposited on the mating surface of one or both of the piezoelectric plate and the device substrate. One or both mating surfaces may be activated using, for example, a plasma process. The mating surfaces may then be pressed together with considerable force to establish molecular bonds between the piezoelectric plate and the device substrate or intermediate material layers.

At 820, the sacrificial substrate may be removed. For example, the piezoelectric plate and the sacrificial substrate may be a wafer of piezoelectric material that has been ion implanted to create defects in the crystal structure along a plane that defines a boundary between what will become the piezoelectric plate and the sacrificial substrate. At 820, the wafer may be split along the defect plane, for example by thermal shock, detaching the sacrificial substrate and leaving the piezoelectric plate bonded to the device substrate. The exposed surface of the piezoelectric plate may be polished or processed in some manner after the sacrificial substrate is detached.

Thin plates of single-crystal piezoelectric materials laminated to a non-piezoelectric substrate are commercially available. At the time of this application, both lithium niobate and lithium tantalate plates are available bonded to various substrates including silicon, quartz, and fused silica. Thin plates of other piezoelectric materials may be available now or in the future. The thickness of the piezoelectric plate may be between 300 nm and 1000 nm. When the substrate is silicon, a layer of SiO₂ may be disposed between the piezoelectric plate and the substrate. When a commercially available piezoelectric plate/device substrate laminate is used, steps 810A, 815, and 820 of the process 800 are not performed.

A first conductor pattern, including IDTs of each XBAR, is formed at 845 by depositing and patterning one or more conductor layers on the front side of the piezoelectric plate. The conductor layer may be, for example, aluminum, an aluminum alloy, copper, a copper alloy, or some other conductive metal. Optionally, one or more layers of other materials may be disposed below (i.e. between the conductor layer and the piezoelectric plate) and/or on top of the conductor layer. For example, a thin film of titanium, chrome, or other metal may be used to improve the adhesion between the conductor layer and the piezoelectric plate. A second conductor pattern of gold, aluminum, copper or other higher conductivity metal may be formed over portions of the first conductor pattern (for example the IDT bus bars and interconnections between the IDTs).

Each conductor pattern may be formed at 845 by depositing the conductor layer and, optionally, one or more other metal layers in sequence over the surface of the piezoelectric plate. The excess metal may then be removed by etching through patterned photoresist. The conductor layer can be etched, for example, by plasma etching, reactive ion etching, wet chemical etching, or other etching techniques.

Alternatively, each conductor pattern may be formed at 845 using a lift-off process. Photoresist may be deposited over the piezoelectric plate. and patterned to define the conductor pattern. The conductor layer and, optionally, one or more other layers may be deposited in sequence over the surface of the piezoelectric plate. The photoresist may then be removed, which removes the excess material, leaving the conductor pattern.

At 850, one or more frequency setting dielectric layer(s) may be formed by depositing one or more layers of dielectric material on the front side of the piezoelectric plate. For example, a dielectric layer may be formed over the shunt resonators to lower the frequencies of the shunt resonators relative to the frequencies of the series resonators. The one or more dielectric layers may be deposited using a conventional deposition technique such as physical vapor deposition, atomic layer deposition, chemical vapor deposition, or some other method. One or more lithography processes (using photomasks) may be used to limit the deposition of the dielectric layers to selected areas of the piezoelectric plate. For example, a mask may be used to limit a dielectric layer to cover only the shunt resonators.

At 855, a passivation/tuning dielectric layer is deposited over the piezoelectric plate and conductor patterns. The passivation/tuning dielectric layer may cover the entire surface of the filter except for pads for electrical connections to circuitry external to the filter. In some instantiations of the process 800, the passivation/tuning dielectric layer may be formed after the cavities in the device substrate are etched at either 810B or 810C.

In a second variation of the process 800, one or more cavities are formed in the back side of the device substrate at 810B. A separate cavity may be formed for each resonator in a filter device. The one or more cavities may be formed using an anisotropic or orientation-dependent dry or wet etch to open holes through the back side of the device substrate to the piezoelectric plate. In this case, the resulting resonator devices will have a cross-section as shown in FIG. 1.

In a third variation of the process 800, one or more cavities in the form of recesses in the device substrate may be formed at 810C by etching the substrate using an etchant introduced through openings in the piezoelectric plate. A separate cavity may be formed for each resonator in a filter device. The one or more cavities formed at 810C will not penetrate through the device substrate, and the resulting resonator devices will have a cross-section as shown in FIG. 3.

Ideally, after the cavities are formed at 810B or 810C, most or all of the filter devices on a wafer will meet a set of performance requirements. However, normal process tolerances will result in variations in parameters such as the thicknesses of dielectric layer formed at 850 and 855, variations in the thickness and line widths of conductors and IDT fingers formed at 845, and variations in the thickness of the PZT plate. These variations contribute to deviations of the filter device performance from the set of performance requirements.

To improve the yield of filter devices meeting the performance requirements, frequency tuning may be performed by selectively adjusting the thickness of the passivation/tuning layer deposited over the resonators at 855. The frequency of a filter device passband can be lowered by adding material to the passivation/tuning layer, and the frequency of the filter device passband can be increased by removing material to the passivation/tuning layer. Typically, the process 800 is biased to produce filter devices with passbands that are initially lower than a required frequency range but can be tuned to the desired frequency range by removing material from the surface of the passivation/tuning layer.

At 860, a probe card or other means may be used to make electrical connections with the filter to allow radio frequency (RF) tests and measurements of filter characteristics such as input-output transfer function. Typically, RF measurements are made on all, or a large portion, of the filter devices fabricated simultaneously on a common piezoelectric plate and substrate.

At 865, global frequency tuning may be performed by removing material from the surface of the passivation/tuning layer using a selective material removal tool such as, for example, a scanning ion mill as previously described. “Global” tuning is performed with a spatial resolution equal to or larger than an individual filter device. The objective of global tuning is to move the passband of each filter device towards a desired frequency range. The test results from 860 may be processed to generate a global contour map indicating the amount of material to be removed as a function of two-dimensional position on the wafer. The material is then removed in accordance with the contour map using the selective material removal tool.

At 870, local frequency tuning may be performed in addition to, or instead of, the global frequency tuning performed at 865. “Local” frequency tuning is performed with a spatial resolution smaller than an individual filter device. The test results from 860 may be processed to generate a map indicating the amount of material to be removed at each filter device. Local frequency tuning may require the use of a mask to restrict the size of the areas from which material is removed. For example, a first mask may be used to restrict tuning to only shunt resonators, and a second mask may be subsequently used to restrict tuning to only series resonators (or vice versa). This would allow independent tuning of the lower band edge (by tuning shunt resonators) and upper band edge (by tuning series resonators) of the filter devices.

After frequency tuning at 865 and/or 870, the filter device is completed at 875. Actions that may occur at 875 include forming bonding pads or solder bumps or other means for making connection between the device and external circuitry (if such pads were not formed at 845); excising individual filter devices from a wafer containing multiple filter devices; other packaging steps; and additional testing. After each filter device is completed, the process ends at 895.

FIG. 9 is a simplified flow chart showing a process 900 for making a filter incorporating XBARs. The process 900 starts at 905 with a substrate and a plate of piezoelectric material and ends at 995 with a completed filter. The flow chart of FIG. 9 includes only major process steps. Various conventional process steps (e.g. surface preparation, cleaning, inspection, baking, annealing, monitoring, testing, etc.) may be performed before, between, after, and during the steps shown in FIG. 9.

The flow chart of FIG. 9 captures two variations of the process 900 for making a filter which differ in when and how cavities are formed in the substrate. The cavities may be formed at steps 810B or 810C. Only one of these steps is performed in each of the two variations of the process 900.

Process steps with reference designators from 815 to 875 are essentially the same as the corresponding steps of the process 800 of FIG. 8. Descriptions of these steps will not be repeated. The significant difference between the process 900 and the process 800 is the RF tests 960 and frequency tuning 965 are performed before the cavities are formed at 810B or 810C. When tuning is performed while the area of the resonators is still attached to the substrate, the substrate provides mechanical support to the piezoelectric plate and acts as a sink for heat generated as material is removed from the passivation/tuning dielectric layer. This avoids damage to the diaphragm that may occur if tuning is done after the cavities are formed, as in the process 800.

Since tuning is performed while the area of the resonators is still attached to the substrate, the RF tests at 960 cannot measure the actual performance parameters of a filter. Instead, the RF tests at 960 measure other parameters that can be correlated with the performance of the filter after the cavities are formed. The RF tests at 960 may measure the resonance frequencies of other acoustic modes that may or may not still exist after the cavities are formed. These modes may include Sezawa modes, Rayleigh modes, and various bulk acoustic modes. For example, the input/output transfer functions of filter devices and/or the admittances of individual resonators may be measured on all, or a large portion, of the filter devices fabricated simultaneously on a common piezoelectric plate and substrate.

The test results from 960 are processed to predict the performance of the filter devices which, in turn, is used to generate a contour map indicating the amount of material to be removed as a function of two-dimensional position on the wafer. For example, a neutral network may be trained to convert the admittance of a resonator over a frequency span from 0 to 1 GHz into a prediction of an amount of material to be removed at a particular location on the contour map.

At 965, the frequency of the filter devices is selectively tuned by removing material from the surface of the passivation/tuning layer in accordance with the contour map generated at 960. The material may be remove using a selective material removal tool such as, for example, a scanning ion mill as previously described. Global and/or local frequency tuning, as previously described, may be performed at 965. After frequency tuning, the process 900 may be completed as previously described with respect to the process 800.

FIG. 10 is a simplified flow chart showing another process 1000 for fabricating a filter device incorporating XBARs. Specifically, the process 1000 is for fabricating a filter device with two or more different piezoelectric diaphragm thicknesses. For example, a device may have different diaphragm thicknesses for series and shunt resonators as shown in FIG. 6B. The process 1000 starts at 1005 with a substrate and a plate of piezoelectric material disposed on a sacrificial substrate and ends at 1095 with a completed filter device. The flow chart of FIG. 10 includes only major process steps. Various conventional process steps (e.g. surface preparation, cleaning, inspection, baking, annealing, monitoring, testing, etc.) may be performed before, between, after, and during the steps shown in FIG. 10.

The flow chart of FIG. 10 captures three variations of the process 1000 for making an XBAR device which differ in when and how cavities are formed in the substrate. The cavities may be formed at steps 810A, 810B, or 810C. Only one of these steps is performed in each of the three variations of the process 1000.

Process steps with reference designators from 815 to 875 are essentially the same as the corresponding steps of the process 800 of FIG. 8. Descriptions of these steps will not be repeated. The significant difference between the process 1000 and the process 800 is the addition of steps 1030 and 1035.

At 1030, selected area of the piezoelectric plate are thinned. For example, areas of the piezoelectric plate that will become the diaphragms of series resonators may be thinned as shown in view E of FIG. 7. The thinning may be done using a scanning material tool such as an ion mill. Alternatively, the areas to be thinned may be defined by a mask and material may be removed using an ion mill, a sputter etching tool, or a wet or dry etching process. In all cases, precise control of the depth of the material removed over the surface of a wafer is required. After thinning, the piezoelectric plate will be divided into regions having two or more different thicknesses.

The surface remaining after material is removed from the piezoelectric plate may be damaged, particularly if an ion mill or sputter etch tool is used at 1030. Some form of post processing, such as annealing or other thermal process may be performed at 1035 to repair the damaged surface.

After the piezoelectric plate is selectively thinned at 1030 and any surface damage is repaired at 1035, the remaining steps of the process 1000 (as shown in FIG. 10) may be the same as the corresponding steps of the process 800, where RF test 860 and frequency tuning 865 occur after the cavities are formed at 810A, 810B, or 810C. Alternatively, the remaining steps of the process 1000 (not shown in FIG. 10) may be the same as the corresponding steps of the process 900, where RF test 960 and frequency tuning 965 occur before the cavities are formed at 810B or 810C. The formation of frequency setting dielectric layers at 850 is not necessarily performed during the process 1000.

FIG. 11 is a simplified flow chart showing another process 1100 for fabricating a filter device incorporating XBARs. Specifically, the process 1100 is for fabricating a filter device with additional steps to improve the thickness uniformity of the piezoelectric plate, as previously illustrated in FIG. 7. The flow chart of FIG. 11 includes only major process steps. Various conventional process steps (e.g. surface preparation, cleaning, inspection, baking, annealing, monitoring, testing, etc.) may be performed before, between, after, and during the steps shown in FIG. 11. Process steps with reference designators from 815 to 875 are essentially the same as the corresponding steps of the process 800 of FIG. 8. Process steps 1030 and 1035 are essentially the same as the corresponding steps of the process 1000 of FIG. 10. Descriptions of these steps will not be repeated.

The flow chart of FIG. 11 captures multiple variations of the process 1100 for making an XBAR which differ in when and how cavities are formed in the substrate and how the frequencies of shunt resonators are offset from the frequencies of series resonators. The cavities may be formed at steps 810B or 810C. Only one of these steps is performed in any variations of the process 1100. The frequencies of shunt resonators may be offset from the frequencies of series resonators by forming a frequency setting dielectric layer over the shunt resonators at 850. Alternatively, the frequencies of shunt resonators may be offset from the frequencies of series resonators by thinning the piezoelectric plate that will form the diaphragms of the series resonators at 1030. One or both of these steps is performed in any variations of the process 1100.

The primary difference between the process 1100 and the previously described processes is the addition of steps 1120 and 1125. At 1120, optical measurements of the piezoelectric plate thickness are made using an optical thickness measurement tool such as, for example, an ellipsometer/reflectometer. The optical thickness measurement tool may measure light reflected from the surface of the piezoelectric plate and from the interface between the piezoelectric plate and the substrate. The reflections from a particular measurement point on the piezoelectric plate may be measured using multiple light wavelengths, incidence angles, and/or polarization states. The results of multiple measurements are processed to determine the thickness of the piezoelectric plate at the measurement point.

The measurement process is repeated to determine the thickness of the piezoelectric plate at multiple measurement points on the surface of the piezoelectric plate. The multiple points may, for example form a grid or matrix of measurement points on the surface of the plate. The measurement data can be processed and interpolated to provide a map of the thickness of the piezoelectric plate.

At 1125, excess material is removed from the piezoelectric plate using a material removal tool, as previously shown in view C of FIG. 7. The material removal tool may be, for example, a scanning ion mill or some other tool. A scanning ion mill scans a beam of high energy ions over the surface of the piezoelectric plate. The incidence of the ion beam on the piezoelectric plate removes material at the surface by sublimation or sputtering. The ion beam may be scanned over the surface of the piezoelectric plate one or more times in a raster pattern. The ion current or the dwell time of the ion beam may be varied during the raster scan to control the depth of material removed from each point on the piezoelectric plate in accordance with the map of the thickness of the piezoelectric plate. The result is a piezoelectric plate with substantially improved thickness uniformity. The thickness at any point on the piezoelectric plate may be substantially equal to a target thickness, as previously defined.

Optionally, portions of the piezoelectric plate destined to become diaphragms of series resonators may be thinned at 1030. Damage to the exposed surface of the piezoelectric plate incurred at 1125 and/or 1030 may be removed by post processing at 1035, as previously described.

The remaining steps of the process 1100 (as shown in FIG. 11) may be the same as the corresponding steps of the process 800, except that forming the frequency setting dielectric layer at 850 may not be performed if the piezoelectric plate is selectively thinned at 1030. In either case, RF test 860 and frequency tuning 865/870 may occur after the cavities are formed at 810B or 810C. Alternatively, the remaining steps of the process 1100 (not shown in FIG. 11) may be the same as the corresponding steps of the process 900, where RF test 960 and frequency tuning 965 occur before the cavities are formed at 810B or 810C.

Closing Comments

Throughout this description, the embodiments and examples shown should be considered as exemplars, rather than limitations on the apparatus and procedures disclosed or claimed. Although many of the examples presented herein involve specific combinations of method acts or system elements, it should be understood that those acts and those elements may be combined in other ways to accomplish the same objectives. With regard to flowcharts, additional and fewer steps may be taken, and the steps as shown may be combined or further refined to achieve the methods described herein. Acts, elements and features discussed only in connection with one embodiment are not intended to be excluded from a similar role in other embodiments.

As used herein, “plurality” means two or more. As used herein, a “set” of items may include one or more of such items. As used herein, whether in the written description or the claims, the terms “comprising”, “including”, “carrying”, “having”, “containing”, “involving”, and the like are to be understood to be open-ended, i.e., to mean including but not limited to. Only the transitional phrases “consisting of” and “consisting essentially of”, respectively, are closed or semi-closed transitional phrases with respect to claims. Use of ordinal terms such as “first”, “second”, “third”, etc., in the claims to modify a claim element does not by itself connote any priority, precedence, or order of one claim element over another or the temporal order in which acts of a method are performed, but are used merely as labels to distinguish one claim element having a certain name from another element having a same name (but for use of the ordinal term) to distinguish the claim elements. As used herein, “and/or” means that the listed items are alternatives, but the alternatives also include any combination of the listed items. 

The invention claimed is:
 1. A filter device, comprising: a substrate having a surface; a single-crystal piezoelectric plate having front and back surfaces, the back surface attached to the surface of the substrate, portions of the single-crystal piezoelectric plate forming a first diaphragm and a second diaphragm spanning respective cavities in the substrate, wherein a first portion of the piezoelectric plate including the first diaphragm has a first thickness, and a front surface of a second portion of the piezoelectric plate, which includes the second diaphragm, is recessed relative to the front surface of the first portion of the piezoelectric plate such that the second diaphragm has a second thickness less than the first thickness; a first resonator comprising a first interdigital transducer (IDT) with interleaved fingers on a front surface of the first diaphragm; and a second resonator comprising a second IDT with interleaved fingers on the front surface of the second diaphragm.
 2. The filter device of claim 1, wherein interleaved fingers of one or more additional IDTs are disposed on respective diaphragms having one of the first thickness and the second thickness.
 3. The filter device of claim 2, wherein each additional IDT is disposed on a respective diaphragm spanning a respective cavity.
 4. The filter device of claim 1, wherein the single-crystal piezoelectric plate and all of the IDTs are configured such that a respective radio frequency signal applied to the first IDT and the second IDT excites a respective shear primary acoustic mode within the respective diaphragm.
 5. The filter device of claim 4, wherein a direction of acoustic energy flow of all of the shear primary acoustic modes is substantially orthogonal to the front and back surfaces of the respective diaphragms.
 6. The filter device of claim 4, wherein the single-crystal piezoelectric plate is one of lithium niobate and lithium tantalate.
 7. The filter device of claim 1, wherein the second thickness is greater than or equal to 200 nm, and the first thickness less than or equal to 1000 nm.
 8. The filter device of claim 1, further comprising: one or more additional diaphragms having respective thicknesses intermediate the first thickness and the second thickness.
 9. The filter device of claim 1, wherein the first resonator is a shunt resonator and the second resonator is a series resonator in a ladder filter circuit.
 10. The filter device of claim 9, further comprising: one or more additional shunt resonators and one or more additional series resonators, wherein the fingers of the IDTs of all of the shunt resonators are on diaphragms having the first thickness, and the fingers of the IDTs of all of the series resonators are on diaphragms having the second thickness.
 11. A method of fabricating a filter device, comprising: attaching a back surface of a piezoelectric plate having opposing front and back surfaces and a first thickness to a surface of a substrate; selectively forming a recess in the front surface of the piezoelectric plate to thin a portion of the piezoelectric plate from the first thickness to a second thickness less than the first thickness; forming cavities in the substrate such that portions of the single-crystal piezoelectric plate form a plurality of diaphragms spanning respective cavities; and forming a conductor pattern on the front surface, the conductor pattern including a plurality of interdigital transducers (IDTs) of a plurality of resonators, wherein interleaved fingers of a first IDT of the plurality of IDTs are on a first diaphragm having the first thickness, and interleaved fingers of at least a second IDT of the plurality of IDTs are on a second diaphragm having the second thickness.
 12. The method of claim 11, further comprising, selectively thinning additional portions of the piezoelectric plate to a third thickness intermediate the first thickness and the second thickness, wherein interleaved fingers of at least a third IDT of the plurality of IDTs are disposed on a diaphragm having the third thickness.
 13. The method of claim 11, further comprising, selectively thinning additional portions of the piezoelectric plate to one or more additional thicknesses intermediate the first thickness and the second thickness.
 14. The method of claim 11, wherein the single-crystal piezoelectric plate and all of the IDTs are configured such that a respective radio frequency signal applied to each IDT excites a respective shear primary acoustic mode within the respective diaphragm.
 15. The method of claim 14, wherein a direction of acoustic energy flow of all of the shear primary acoustic modes is substantially orthogonal to the front and back surfaces of the respective diaphragms.
 16. The method of claim 14, wherein the single-crystal piezoelectric plate is one of lithium niobate and lithium tantalate.
 17. The method of claim 11, wherein the second thickness is greater than or equal to 200 nm, and the first thickness less than or equal to 1000 nm.
 18. The method of claim 11, wherein each of the plurality of IDTs is disposed on a respective diaphragm spanning a respective cavity.
 19. The method of claim 11, wherein the plurality of resonators includes at least one shunt resonator and at least one series resonator, the fingers of the IDT of the at least one shunt resonator are disposed on a diaphragm having the first thickness, and the fingers of the IDT of the at least one series resonator are disposed on a diaphragm having the second thickness.
 20. The method of claim 11, wherein the plurality of resonators includes a plurality of shunt resonators and a plurality of series resonators, the fingers of the IDTs of all of the shunt resonators are disposed on diaphragms having the first thickness, and the fingers of the IDTs of all of the series resonators are disposed on diaphragms having the second thickness. 